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Q. 103

Expert-verified
Found in: Page 430

### The Practice of Statistics for AP Examination

Book edition 6th
Author(s) Daren Starnes, Josh Tabor
Pages 837 pages
ISBN 9781319113339

# Lefties Refer to Exercise 99. a. Justify why L can be approximated by a Normal distribution. b. Use a Normal distribution to estimate the probability that 15 or more students in the sample are left-handed.

1. The $L$ is about regularly distributed.
2. The resultant probability is $0.1003.$
See the step by step solution

## Part (a) Step 1: Given information

The number of students $\left(n\right)=100$

Left-handed students as a percentage of total students $\left(p\right)=0.11$

## Part (a) Step 2: Calculation

Consider,

$np=100\left(0.11\right)=11>10\phantom{\rule{0ex}{0ex}}n\left(1-p\right)=100\left(1-0.11\right)=89>10$

Therefore, the L is about regularly distributed.

## Part (b) Step 1: Given information

The number of students $\left(n\right)=100$

Left-handed students as a percentage of total students$\left(p\right)=0.11$

## Part (b) Step 2: Calculation

If 15 or more pupils are left-handed, the probability is calculated as"

$\begin{array}{rcl}P\left(X& \ge & 15\right)=P\left(Z\ge \frac{15-100\left(0.11\right)}{\sqrt{100\left(0.11\right)\left(1-0.11\right)}}\right)\\ & =& P\left(Z\ge 1.28\right)\\ & =& 1-0.8997\\ & =& 0.1003\end{array}$

Thus, the resultant probability is 0.1003.